Non existent probably. I doubt a King would be allowed to marry a man. Kings/Royals have had to abdicate/renounce their right to the throne to marry people of other religions etc, and with many places in the world, including the USA struggling to accept gay marriage among regular people, it's definitely not going to go down well in a Royal family!

Well, royalty is generally expected to reproduce. However, it is not uncommon for kings and queens in ancient and modern societies alike to have consorts or concubines who may or may not be members of the same sex.